Cryopreservation (freezing) of human gametes (unfertilized egg) provides a great potential to preserve or extend fertility in the face of disease and social circumstances (cancer diagnosis, delaying childbirth, single women, etc.). There are two methods for storage of oocytes (unfertilized eggs): slow freezing or vitrification (uses higher concentrations of cryoprotectant and faster cooling rates). Slow freezing is the standard method and has been successful for embryos since 1983 and more recently for oocytes. Recent reports indicate that vitrification may be more successful than slow freezing. The aim of this study is to examine the rate at which frozen eggs survive freezing and thawing, the rate at which the frozen/thawed eggs fertilize with sperm and the pregnancy outcomes of oocyte (egg) vitrification cycles to determine whether the outcomes are similar or better than standard oocyte (egg) cryopreservation (freezing) cycles.